Typically, position/location estimates include some errors. For example, RF trilateration methods use estimated ranges from multiple receivers to estimate the location of an object. RF triangulation uses the angles at which the RF signals arrive at multiple receivers to estimate the location of the object. However, many obstructions, such as barriers, clouds, landscape objects, and the like can distort the estimated range and angle readings leading to varied qualities of location estimate. Estimation-based locating is often measured in accuracy for a given confidence level. In other words, how frequently an observed interval contains the desired parameter is determined by the confidence level (confidence coefficient). More specifically, if confidence intervals are constructed across many separate data analyses of repeated (and possibly different) experiments, the proportion of such intervals that contain the true value of the parameter will match the confidence level.
A confidence region is a multi-dimensional generalization of a confidence interval, that is, a set of points in an n-dimensional space, which is often represented as an ellipsoid around a point which is an estimated solution to a problem, for example, a set of location estimates. In a two-dimensional space, confidence region is represented as an ellipse. The confidence region is calculated in such a way that if a set of measurements were repeated many times and a confidence region calculated in the same way on each set of measurements, then a certain percentage of the time, on average the confidence region would include the point representing the “true” values of the set of variables being estimated, for example, a set of location estimates. Such an elliptical confidence region is conventionally referred to as an elliptical error probability (EEP).
Current position estimation approaches do not predict a future position of a moving object. Instead, they typically only provide a point estimate of the location along with parameters of an EEP at a particular level of confidence (e.g. 95%).
Moreover, in many situations, it is impractical to directly observe where a moving object is and to where it may be traveling.
Accordingly, there is a need for a method for determining the future position boundary of a moving object, which utilizes the already determined two previous location estimates. Each of the two previous location estimates being represented by an elliptical error probability (EEP).